Engineering HydrologyEngineering HydrologyHYD 301.3HYD 301.3

Dr. Hari Krishna ShresthaDr. Hari Krishna ShresthaAssociate Professor, Dept. of Civil Engineering, Nepal Engineering CollegeAssociate Professor, Dept. of Civil Engineering, Nepal Engineering College

Director, Center for Disaster Risk StudiesDirector, Center for Disaster Risk StudiesContact: Contact: shrestha_h@hotmail.com

June 2007June 2007

Chapter 2Chapter 2Evapotranspiration (ET) Factors Evapotranspiration (ET) Factors (4 hours)(4 hours)

The meteorological factors determining evapotranspiration are The meteorological factors determining evapotranspiration are weather parameters which provide energy for vaporization and weather parameters which provide energy for vaporization and remove water vapor from the evaporating surface. The principal remove water vapor from the evaporating surface. The principal

weather parameters to consider are:weather parameters to consider are: 2.1 Solar Radiation2.1 Solar Radiation 2.2 Air Temperature2.2 Air Temperature 2.3 Air Humidity2.3 Air Humidity 2.4 Wind Speed2.4 Wind Speed

2.5 Evaporation2.5 Evaporation 2.6 Transpiration2.6 Transpiration 2.7 Penman’s Equation2.7 Penman’s Equation

Humidity

ET

Solar RadiationAir Temperature

Wind Speed

ET

2.12.1 RadiationRadiation

Radiation: a mode of heat transfer by Radiation: a mode of heat transfer by electromagnetic waveselectromagnetic waves

Solar Radiation can be termed as the fuel Solar Radiation can be termed as the fuel essential for operation of the engine that drives essential for operation of the engine that drives the hydrologic cycle. Solar radiation determine the hydrologic cycle. Solar radiation determine weather and climate of earth. weather and climate of earth.

Radiation is emission of heat energy. When Radiation is emission of heat energy. When the earth is at mean distance from the sun, the the earth is at mean distance from the sun, the rate (intensity) at which solar radiation reaches rate (intensity) at which solar radiation reaches the upper limits of earth’s atmosphere on a the upper limits of earth’s atmosphere on a surface normal to the incident radiation is surface normal to the incident radiation is called solar constant (1374 W/mcalled solar constant (1374 W/m22).).

TerminologyTerminology:: Insolation: incident solar radiationInsolation: incident solar radiation Albedo: ratio of the amount of solar radiation reflected by a surface Albedo: ratio of the amount of solar radiation reflected by a surface

to the amount incident up on it (%)to the amount incident up on it (%) Reflectivity: ratio of the amount of electromagnetic radiation Reflectivity: ratio of the amount of electromagnetic radiation

reflected by a body to the amount incident up on it (%)reflected by a body to the amount incident up on it (%)Very little of earth’s surface is normal to incident solar radiation. This Very little of earth’s surface is normal to incident solar radiation. This

irregularity of earth surface causes variation in heat absorption by irregularity of earth surface causes variation in heat absorption by the earth surface at different location. This difference in insolation is the earth surface at different location. This difference in insolation is one of the primary factors in determining global circulation of the one of the primary factors in determining global circulation of the earth’s atmosphere.earth’s atmosphere.

Actinometers and radiometers are used to measure intensity of radiant Actinometers and radiometers are used to measure intensity of radiant energy. The data is used in studies of evaporation and snowmelt.energy. The data is used in studies of evaporation and snowmelt.

Radiation BalanceRadiation Balance

Source: USGS

Heat Balance of Earth’s Surface and AtmosphereHeat Balance of Earth’s Surface and Atmosphere

Earth’s RadiationSolar Radiation

6 + 64 = 70 LW

51 absorbed by surface of earth

30 reflected

100 (340 W/m2)

15 absorbed by atmosphere

21 (LW)

30 heat flux

Emission by clouds

19 absorbed

2.22.2 TemperatureTemperature

Temperature is a measure of hotness Temperature is a measure of hotness of an object. Air temperature directly of an object. Air temperature directly affects the evapotranspiration from a affects the evapotranspiration from a basin and hence affects the water basin and hence affects the water balance. Temperature of atmospheric balance. Temperature of atmospheric air decreases at an average rate of air decreases at an average rate of about 6˚C per 1000 m increase in about 6˚C per 1000 m increase in altitude within the troposphere, but is altitude within the troposphere, but is relatively constant in the lower part of relatively constant in the lower part of the stratosphere.the stratosphere.

TerminologiesTerminologies Average (or Mean) Temperature:Average (or Mean) Temperature: Arithmetic mean temperature for a given period Arithmetic mean temperature for a given period Mean Daily Temperature: Average of hourly temperature, if hourly data are availableMean Daily Temperature: Average of hourly temperature, if hourly data are available

Average of temperature data at pre-specified times, if data of only certain times are availableAverage of temperature data at pre-specified times, if data of only certain times are availableAverage of the daily max and min temperature, if only maximum and minimum data are available Average of the daily max and min temperature, if only maximum and minimum data are available

Normal Temperature: Arithmetic mean temperature based on previous 30 years’ dataNormal Temperature: Arithmetic mean temperature based on previous 30 years’ data Normal Daily Temperature: The average mean daily temperature of a given date computed for a Normal Daily Temperature: The average mean daily temperature of a given date computed for a

specific 30-year period.specific 30-year period. Lapse Rate: The rate at which temperature decreases with increase in altitude through free and Lapse Rate: The rate at which temperature decreases with increase in altitude through free and

undisturbed airundisturbed air Inversion (or temperature inversion): It is a negative lapse rate, i.e., temperature increases with Inversion (or temperature inversion): It is a negative lapse rate, i.e., temperature increases with

altitude. This condition usually occurs on still, clear nights because there is little turbulent mixing altitude. This condition usually occurs on still, clear nights because there is little turbulent mixing of air and because outgoing radiation is unhampered by clouds.of air and because outgoing radiation is unhampered by clouds.

Mean monthly Temperature: It is the average of the mean monthly maximum and minimum Mean monthly Temperature: It is the average of the mean monthly maximum and minimum temperature.temperature.

Mean Annual Temperature: It is the average of the monthly means for the year.Mean Annual Temperature: It is the average of the monthly means for the year. Degree Day: It is a departure of one degree for one day in the mean daily temperature from a Degree Day: It is a departure of one degree for one day in the mean daily temperature from a

specified base temperature.specified base temperature. Dew Point: The dew point is the temperature at which the air mass just becomes saturated if Dew Point: The dew point is the temperature at which the air mass just becomes saturated if

cooled at constant pressure with moisture neither added nor removed.cooled at constant pressure with moisture neither added nor removed. Dry Adiabatic Lapse Rate: Rate of decrease in temperature of a air parcel due to increase in Dry Adiabatic Lapse Rate: Rate of decrease in temperature of a air parcel due to increase in

volume when it rises in altitude. The value of dry adiabatic lapse rate is 1 ˚Cvolume when it rises in altitude. The value of dry adiabatic lapse rate is 1 ˚C per 100 m.per 100 m. Adiabatic Saturation Lapse Rate: When air parcel rises beyond the condensation level the lapse Adiabatic Saturation Lapse Rate: When air parcel rises beyond the condensation level the lapse

rate is lower (0.3 to 1 degree Celsius per 100 m) due to the addition of latent heat of rate is lower (0.3 to 1 degree Celsius per 100 m) due to the addition of latent heat of condensation on the rising air parcel. This lower lapse rate is Adiabatic Saturation Lapse Rate condensation on the rising air parcel. This lower lapse rate is Adiabatic Saturation Lapse Rate (also known as moist (or wet) adiabatic lapse rate).(also known as moist (or wet) adiabatic lapse rate).

Temperature measurement Temperature measurement

The thermometers used to measure temperature The thermometers used to measure temperature must be placed where air circulation is relatively must be placed where air circulation is relatively unobstructed, and yet they must be protected unobstructed, and yet they must be protected from the direct rays of the sun and from from the direct rays of the sun and from precipitation. Also, all thermometers should be precipitation. Also, all thermometers should be placed at the same height above the ground for placed at the same height above the ground for the recorded temperatures to be comparable. the recorded temperatures to be comparable. The maximum-minimum thermometers are used The maximum-minimum thermometers are used to record daily maximum and minimum to record daily maximum and minimum temperature.temperature.

Factors Affecting TemperatureFactors Affecting Temperature

The temperature of a locality is a complex The temperature of a locality is a complex function of several variables such as function of several variables such as latitude, altitude, ocean currents, distance latitude, altitude, ocean currents, distance from sea, winds, cloud cover, and aspect from sea, winds, cloud cover, and aspect (land slope and its orientation).(land slope and its orientation).

2.3 Humidity2.3 Humidity Humidity is the state of atmosphere in relation to amount Humidity is the state of atmosphere in relation to amount

of water vapor it contains. Humidity is closely related to of water vapor it contains. Humidity is closely related to its temperature – higher the air temperature, more vapor its temperature – higher the air temperature, more vapor the air can hold. For this reason, saturation vapor the air can hold. For this reason, saturation vapor pressure (epressure (eww) goes up with air temperature; i.e., as ) goes up with air temperature; i.e., as temperature goes up etemperature goes up eww also goes up. also goes up.

Significance of HumiditySignificance of Humidity: The amount of water vapor in : The amount of water vapor in air effectively controls the weather condition by air effectively controls the weather condition by controlling evapotranspiration from land and water controlling evapotranspiration from land and water surfaces. Evaporation rate is proportional to difference surfaces. Evaporation rate is proportional to difference between saturated vapor pressure at water temperature between saturated vapor pressure at water temperature (e(eww) and actual vapor pressure in air (e) and actual vapor pressure in air (eaa). ).

EEL = C (e = C (eww – e – eaa),),where, Ewhere, EL is lake evaporation rate, C is a constant of is lake evaporation rate, C is a constant of proportionality.proportionality.

Causes of HumidityCauses of Humidity::

Molecules of water having sufficient kinetic energy to overcome Molecules of water having sufficient kinetic energy to overcome attractive forces tending to hold them within the body of liquid water attractive forces tending to hold them within the body of liquid water are projected through the water surface into the air. The process by are projected through the water surface into the air. The process by which liquid water is converted into vapor is called which liquid water is converted into vapor is called vaporizationvaporization or or evaporationevaporation. Since the kinetic energy increases and surface tension . Since the kinetic energy increases and surface tension decrease as temperature rises, evaporation rate increases with decrease as temperature rises, evaporation rate increases with temperature.temperature.

Most of the atmospheric vapor is the product of evaporation from Most of the atmospheric vapor is the product of evaporation from water surfaces. The direct transformation from ice to vapor, and vice water surfaces. The direct transformation from ice to vapor, and vice versa, is called versa, is called sublimationsublimation. The process by which vapor changes . The process by which vapor changes to the liquid or solid state is called to the liquid or solid state is called condensationcondensation. .

Rise in air temperature

Rise in kinetic energy of air molecules within water body

Decrease in surface tensionforces

Evaporation

Solar radiation Water vapor

Properties of Water VaporProperties of Water Vapor The partial pressure exerted by water vapor is called The partial pressure exerted by water vapor is called vapor pressurevapor pressure (e). If all the water (e). If all the water

vapor in a closed container of moist air with an initial total pressure p were removed, then vapor in a closed container of moist air with an initial total pressure p were removed, then the final pressure p’ of dry air alone would be less than p. Then, e = p – p’the final pressure p’ of dry air alone would be less than p. Then, e = p – p’

When the maximum amount of water vapor for a given temperature is contained in a When the maximum amount of water vapor for a given temperature is contained in a given space, the space is saturated with water vapor. The pressure exerted in a given space, the space is saturated with water vapor. The pressure exerted in a saturated space is called saturated space is called saturation vapor pressure (esaturation vapor pressure (eww)), which is the maximum vapor , which is the maximum vapor pressure possible at a given temperature. epressure possible at a given temperature. eww = f (air temperature) = f (air temperature)

Vaporization removes heat from liquid being vaporized, while condensation adds heat. Vaporization removes heat from liquid being vaporized, while condensation adds heat. Vaporization is the reason for feeling colder on a hot day when we stand in front of a fan. Vaporization is the reason for feeling colder on a hot day when we stand in front of a fan. Vaporization of sweat molecules removes heat from sweat on our skin. The Vaporization of sweat molecules removes heat from sweat on our skin. The latent heat latent heat of vaporizationof vaporization is the amount of heat absorbed by a unit mass of a substance, without is the amount of heat absorbed by a unit mass of a substance, without change in temperature, which passing from liquid to vapor state. A change from vapor change in temperature, which passing from liquid to vapor state. A change from vapor state to liquid state releases equal amount of heat. state to liquid state releases equal amount of heat. Latent heat of vaporization (Latent heat of vaporization ())

The latent heat of vaporization, The latent heat of vaporization, , expresses the energy required to , expresses the energy required to change a unit mass of water from liquid to water vapor in a constant change a unit mass of water from liquid to water vapor in a constant pressure and constant temperature process. The value of the latent heat pressure and constant temperature process. The value of the latent heat varies as a function of temperature. At a high temperature, less energy varies as a function of temperature. At a high temperature, less energy will be required than at lower temperatures. As will be required than at lower temperatures. As varies only slightly over varies only slightly over normal temperature ranges a single value of 2.45 MJ kgnormal temperature ranges a single value of 2.45 MJ kg-1-1 is taken in the is taken in the simplification of the FAO Penman-Monteith equation. This is the latent simplification of the FAO Penman-Monteith equation. This is the latent heat for an air temperature of about 20°C.heat for an air temperature of about 20°C. Source: FAOSource: FAO

Properties of Water VaporProperties of Water Vapor (continued) (continued)

The The heat of vaporization of waterheat of vaporization of water (Hv) varies with temperature, but can be (Hv) varies with temperature, but can be determined accurately up to 40°C by determined accurately up to 40°C by

Hv = 2.50 – 0.00236 T (Hv is in kilojoules per gram, and T is in degree Hv = 2.50 – 0.00236 T (Hv is in kilojoules per gram, and T is in degree Celsius) or byCelsius) or by

Hv = 597.3 – 0.564 T (Hv is in calories per gram, and T is in degree Hv = 597.3 – 0.564 T (Hv is in calories per gram, and T is in degree Celsius).Celsius).

The The latent heat of fusionlatent heat of fusion for water is the amount of heat required to for water is the amount of heat required to convert one gram of ice to liquid water at same temperature. When one convert one gram of ice to liquid water at same temperature. When one gram of liquid water at 0°C freezes into ice at same temperature, the latent gram of liquid water at 0°C freezes into ice at same temperature, the latent heat of fusion (0.337 kJ/g or ≈ 80 cal/g) is liberated.heat of fusion (0.337 kJ/g or ≈ 80 cal/g) is liberated.

The The latent heat of sublimationlatent heat of sublimation for water is the amount of heat required to for water is the amount of heat required to convert one gram of ice into vapor at same temperature without passing convert one gram of ice into vapor at same temperature without passing through intermediate liquid state. It is equal to the sum of the latent heat of through intermediate liquid state. It is equal to the sum of the latent heat of vaporization and latent heat of fusion. At 0°C the latent heat of sublimation vaporization and latent heat of fusion. At 0°C the latent heat of sublimation for water is about 2.837 kJ/g (2.5 + 0.337). Direct condensation of vapor for water is about 2.837 kJ/g (2.5 + 0.337). Direct condensation of vapor into ice at same temperature liberated an equivalent amount of heat ( ≈ 677 into ice at same temperature liberated an equivalent amount of heat ( ≈ 677 cal/g). The value of 677 comes from the addition of 597.3 and 80.cal/g). The value of 677 comes from the addition of 597.3 and 80.

Measures of Atmospheric MoistureMeasures of Atmospheric Moisture

Commonly used measures of humidity: Commonly used measures of humidity: Vapor pressureVapor pressure Absolute humidity Absolute humidity Specific humidity Specific humidity Mixing ratio Mixing ratio Relative humidityRelative humidity Dew pointDew point

Vapor PressureVapor Pressure

One of the empirical equations used to calculate One of the empirical equations used to calculate vapor pressure (e) is:vapor pressure (e) is:

e = ee = eww – (0.000367) (5 p /9) (T – T – (0.000367) (5 p /9) (T – Tww) [1 + (5 T) [1 + (5 Tww – 448)/14139] – 448)/14139]

where,where,

T and TT and Tww are dry- and wet-bulb temperature (°C) are dry- and wet-bulb temperature (°C) of a psychrometer consisting of two of a psychrometer consisting of two thermometers,thermometers,

eeww is the saturation vapor pressure (mb) is the saturation vapor pressure (mb) corresponding to Tcorresponding to Tww, and , and

p is the atmospheric pressure (mb).p is the atmospheric pressure (mb).

Atmospheric pressure (P)Atmospheric pressure (P)

The atmospheric pressure, P, is the pressure exerted by the weight of the The atmospheric pressure, P, is the pressure exerted by the weight of the earth's atmosphere. Evaporation at high altitudes is promoted due to low earth's atmosphere. Evaporation at high altitudes is promoted due to low atmospheric pressure as expressed in the psychrometric constant. The atmospheric pressure as expressed in the psychrometric constant. The effect is, however, small and in the calculation procedures, the average effect is, however, small and in the calculation procedures, the average value for a location is sufficient. A simplification of the ideal gas law, value for a location is sufficient. A simplification of the ideal gas law, assuming 20°C for a standard atmosphere, can be employed to calculate P: assuming 20°C for a standard atmosphere, can be employed to calculate P:

where,where, P atmospheric pressure [kPa],P atmospheric pressure [kPa],

z elevation above sea level [m],z elevation above sea level [m],

Absolute and Specific HumidityAbsolute and Specific Humidity

Absolute HumidityAbsolute Humidity: It is the mass of water : It is the mass of water vapor contained in a unit volume of air at any vapor contained in a unit volume of air at any instant. instant. ρw = 217 (e/T) where e is in mb and T is in °C.ρw = 217 (e/T) where e is in mb and T is in °C.

Specific HumiditySpecific Humidity (q): It is the mass of water (q): It is the mass of water vapor per unit mass of moist air.vapor per unit mass of moist air.q = (0.622 e) / (p – 0.378 e) ≈ 0.622 e /p, q = (0.622 e) / (p – 0.378 e) ≈ 0.622 e /p, where e = vapor pressure (mb) and where e = vapor pressure (mb) and p = total pressure of the moist air (mb).p = total pressure of the moist air (mb).

Relative HumidityRelative Humidity

It is the percentage ratio between the actual vapor pressure (e) and It is the percentage ratio between the actual vapor pressure (e) and the saturation vapor pressure (ethe saturation vapor pressure (eww) at the same temperature. The ) at the same temperature. The relative humidity is not a direct measure of moisture in air. relative humidity is not a direct measure of moisture in air. H = 100 (e/eH = 100 (e/eww))H = [(112 – 0.1 T + TH = [(112 – 0.1 T + Tdd)/(112 + 0.9 T)])/(112 + 0.9 T)]88

The relative humidity may also be defined as the percentage ratio The relative humidity may also be defined as the percentage ratio between the amount of water vapor actually contained per unit between the amount of water vapor actually contained per unit volume and the amount of water vapor that it can hold at the same volume and the amount of water vapor that it can hold at the same temperature when saturated.temperature when saturated.

Relation between relative humidity, air temperature and dew point Relation between relative humidity, air temperature and dew point temperature:temperature:

T–Td ≈ (14.55+0.1147 T) (1 – H) + [(2.5+0.007 T) (1– T–Td ≈ (14.55+0.1147 T) (1 – H) + [(2.5+0.007 T) (1– H)]H)]33 + [(15.9 + 0.117 T) (1–H)] + [(15.9 + 0.117 T) (1–H)]1414

where, T is in °C and H is in decimal fraction. This relation is correct where, T is in °C and H is in decimal fraction. This relation is correct within 0.3°C.within 0.3°C.

Dew pointDew point

Dew pointDew point: It is the temperature at which the : It is the temperature at which the space becomes saturated when air is cooled space becomes saturated when air is cooled under constant pressure and with constant water under constant pressure and with constant water vapor content. It is the temperature having vapor content. It is the temperature having saturation vapor pressure esaturation vapor pressure eww = existing vapor = existing vapor pressure e.pressure e.

Mixing Ratio (wMixing Ratio (wrr): The mixing ratio is the mass of ): The mixing ratio is the mass of water vapor per unit mass of perfectly dry air in water vapor per unit mass of perfectly dry air in a humid mixture. wa humid mixture. wrr = 0.622 e/p (?) = 0.622 e/p (?)

Depth of precipitable waterDepth of precipitable water: It is the amount of : It is the amount of water vapor in a layer of air.water vapor in a layer of air.

2.42.4 Wind SpeedWind SpeedWind is a moving air. Wind is one of the major factors that affect the climate Wind is a moving air. Wind is one of the major factors that affect the climate and evapotranspiration rate from water surface. Higher wind speed results and evapotranspiration rate from water surface. Higher wind speed results in higher ET rate from a water surface as the wind replaces saturated air in higher ET rate from a water surface as the wind replaces saturated air just above the water surface by unsaturated air.just above the water surface by unsaturated air.

Source: FAO Corporate Document Repository

Types of WindTypes of WindBasically there are Basically there are six types of windsix types of wind..

a) a) Sea and land breezesSea and land breezes: See breeze is the blowing of wind from sea to : See breeze is the blowing of wind from sea to land due to higher temperature (lower atmospheric pressure) at land during land due to higher temperature (lower atmospheric pressure) at land during day time. Sea breeze is the reason we feel cooler near large water body at day time. Sea breeze is the reason we feel cooler near large water body at day time in a hot day. Land breeze is the blowing of wind from land to sea day time in a hot day. Land breeze is the blowing of wind from land to sea due to quicker cooling of land, and hence denser air above land surface.due to quicker cooling of land, and hence denser air above land surface.

b) b) Monsoon (seasonal) WindsMonsoon (seasonal) Winds: Winds whose direction depends on season.: Winds whose direction depends on season. c) c) CycloneCyclone: Cyclones are caused when a low pressure area is surrounded : Cyclones are caused when a low pressure area is surrounded

by high pressure areas. A cyclone is generally followed by heavy rain.by high pressure areas. A cyclone is generally followed by heavy rain. d) d) AnticycloneAnticyclone: Anticyclones result when low areas surround a high : Anticyclones result when low areas surround a high

pressure area. pressure area. e) e) TornadoesTornadoes: Tornadoes are similar to cyclone, but they generally form : Tornadoes are similar to cyclone, but they generally form

over ocean. Tornadoes are generally destructive to land and property.over ocean. Tornadoes are generally destructive to land and property. f) f) Local windsLocal winds: They affect only limited areas and blow for short durations. : They affect only limited areas and blow for short durations.

The cause of local winds is mostly local temperature depressions,The cause of local winds is mostly local temperature depressions,

Wind MeasurementsWind Measurements The wind direction is the direction from which it is blowing. Wind The wind direction is the direction from which it is blowing. Wind

direction is usually expressed in terms of 16 compass points (N, direction is usually expressed in terms of 16 compass points (N, NNE, NE, NEE, E, SEE, SE, SSE, S, SSW, SW, SWW, W, NWW, NNE, NE, NEE, E, SEE, SE, SSE, S, SSW, SW, SWW, W, NWW, NW, NNW) for surface winds and for winds aloft in degrees from NW, NNW) for surface winds and for winds aloft in degrees from North, measured clockwise. Wind speed is given in KPH or knots (1 North, measured clockwise. Wind speed is given in KPH or knots (1 knot = 1.143 miles per hours). Wind speed is measured by knot = 1.143 miles per hours). Wind speed is measured by anemometers. For comparable data, all anemometers are installed anemometers. For comparable data, all anemometers are installed at same elevation above ground. Wind speed varies greatly with at same elevation above ground. Wind speed varies greatly with height above the ground due to ground friction, trees, buildings and height above the ground due to ground friction, trees, buildings and other obstacles. Approximate adjustment for anemometers set at other obstacles. Approximate adjustment for anemometers set at different height above ground is different height above ground is (V/V(V/V00) = (Z/Z) = (Z/Z00)k where V is the wind speed at height Z above the )k where V is the wind speed at height Z above the ground, Vground, V00 = Wind speed at anemometer level Z = Wind speed at anemometer level Z00, k = 1/7., k = 1/7.

Wind RoseWind Rose:: The wind rose is a diagrammatic representation of the wind data The wind rose is a diagrammatic representation of the wind data

(direction and speed). There are many types of wind roses. (direction and speed). There are many types of wind roses.

Types of Types of Wind Wind rosesroses

EvaporationEvaporation

A) Measurement of EvaporationA) Measurement of Evaporation Class A PanClass A Pan ISI Standard PanISI Standard Pan Colorado Sunken PanColorado Sunken Pan USGS Floating PanUSGS Floating PanPan Coefficient (CPan Coefficient (Cpp))Lake Evaporation = CLake Evaporation = Cpp × Pan evaporation × Pan evaporation

B) Empirical Evaporation EquationsB) Empirical Evaporation Equationsa)a) Meyer’s Formula: EMeyer’s Formula: ELL = K = KMM (e (eww-e-eaa)(1+u)(1+u99/16)/16)b)b) Rohwer’s Formula: ERohwer’s Formula: ELL = 0.771 (1.465 – 0.000732 p = 0.771 (1.465 – 0.000732 paa))

(0.44+0.0733 u(0.44+0.0733 u00) (e) (eww-e-eaa))

EvaporationEvaporation

C) Analytical Methods of EvaporationC) Analytical Methods of Evaporation Water Budget MethodWater Budget Method

EELL = P + (V = P + (Visis - V - Vosos) + (V) + (Vigig - V - Vogog) – T) – TLL - - SS Energy-balance MethodEnergy-balance Method

HHnn = H = Haa + H + Hee + H + Hgg + H + Hss + H + Hii

HHnn = H = Hcc (1-r) – H (1-r) – Hbb

HHee = = L E L ELL

EELL = (H = (Hnn – H – Hgg – H – Hss - H - Hii)/[)/[ L (1 + L (1 + )])] = Ha / = Ha / L E L ELL = 6.1×10 = 6.1×10-4-4 p paa (T (Tww-T-Taa)/(e)/(eww-e-eaa))

Mass-transfer MethodMass-transfer Method

EvapotranspirationEvapotranspiration

Potential Evapotranspiration (PET)Potential Evapotranspiration (PET) Actual Evapotranspiration (AET)Actual Evapotranspiration (AET) AET≤ PETAET≤ PET AET = PET when plenty of water is availableAET = PET when plenty of water is available Consumptive useConsumptive use Field capacityField capacity Permanent wilting pointPermanent wilting point Available waterAvailable water Measurement of Evapotranspiration:Measurement of Evapotranspiration: A) LysimeterA) Lysimeter B) Field PlotsB) Field Plots

Penman Equation to Estimate Penman Equation to Estimate Potential Evapotranspiration (PET)Potential Evapotranspiration (PET)

PET = [A HPET = [A Hnn + E + Eaa ] / [A + ] / [A + ]] PET = Daily Potential Evapotranspiration rate (mm/day)PET = Daily Potential Evapotranspiration rate (mm/day) A = slope of the saturation vapor pressure vs. temperature curve at the mean air A = slope of the saturation vapor pressure vs. temperature curve at the mean air

temperature, mmHg/°Ctemperature, mmHg/°C HHnn = net radiation of mm evaporable water per day = net radiation of mm evaporable water per day EEaa = parameter including wind velocity and saturation deficit = 0.35(1+u = parameter including wind velocity and saturation deficit = 0.35(1+u22/160)(e/160)(eww-e-eaa)) = psychrometric constant = 0.49 mm Hg/°C= psychrometric constant = 0.49 mm Hg/°C HHnn = A + B + C = A + B + C A = HA = Haa (1-r) (a + b c) (1-r) (a + b c) B = B = T Taa

44 (0.56 – 0.092 √e (0.56 – 0.092 √eaa)) C = (0.10 + 0.90 c)C = (0.10 + 0.90 c) a = constant depending on latitude a = constant depending on latitude , a = 0.29 cos , a = 0.29 cos b = 0.52b = 0.52 c = n/N, n = actual duration of bright sunshine, N = maximum potential duration of c = n/N, n = actual duration of bright sunshine, N = maximum potential duration of

sunshinesunshine r = albedo = reflection coefficientr = albedo = reflection coefficient eeww = saturation vapor pressure, u = saturation vapor pressure, u22 = wind speed at 2 meters above ground = wind speed at 2 meters above ground The values of A, HThe values of A, Haa, N, and e, N, and eww are normally can be found in standard textbooks are normally can be found in standard textbooks